(preliminary draft – comments welcome) - Stanford … for call/ho...in informing the model. Section four presents the basic model of apologies with exogenous costs. Section five

A Theory of Apologies (preliminary draft – comments welcome) Benjamin Ho*

Stanford Graduate School of Business Revised: March 2005 First Draft: May 2003 ABSTRACT Apologies are a previously unstudied social institution integral in the maintenance of relationships within society. Their application ranges from corporate culture to political systems to legal settings and beyond. This paper formulates a game theoretic signaling model using rational agents that serves as a framework for understanding apologies and their use. The base model uses costly signaling, but further models use cheap talk, where signaling is achieved by a multi-dimensional type-space based on status or empathy. A positive explanation of the fundamental attribution error from social psychology is also provided.

* Thanks to Edward Lazear for excellent advising, as well as Douglas Bernheim for comments.

1 Introduction Paul had a problem. Several weeks ago he made a date to play tennis with his friend Amy at noon on Saturday. Paul arrived at the courts right on time, but Amy shows up one hour late. Paul is angry but after Amy apologies profusely, Paul readily forgives her and they both enjoy the tennis match. They make a date for the following week, whereupon Amy is again late, again apologizes, and again is forgiven. On the third week, Amy is late once more, and at this point Paul is fed up. Talk is cheap, why do apologies have any meaning?1

A common opening for papers about apologies across the social sciences is

to note the dearth of articles about apologies in their respective field. I will begin

no differently. A search of Econ-lit produces no results on the subject of

apologies, yet this social institution has wide ranging significance. Beyond the

use of apologies in daily interpersonal interactions, apologies appear in

organizational design, political reputations, legal litigation, international

relations, corporate governance, and beyond. In an interconnected world where

economic actors are all embedded in a network of relationships (Granovetter

1985; Sen 1977; etc.), apologies act to restore frayed connections.

My approach is to develop a rational choice framework to understand

apologies in a principal-agent context. I avoid behavioral/psychological

assumptions and primarily limit my analysis to preference for consumption, as

this allows applicability to potentially highly rational actors such as politicians

and governments. I argue that apologies exist to maintain relationships. However,

if apologies help relations, talk is cheap, why is it that not everybody apologizes?

This paper focuses on interactions where exogenous factors makes payments

infeasible, whether, for example, because of legal reasons—the inability for a

politician to bribe the electorate for example—or because of social norms—gifts

between friends tend to be limited to symbolic gestures. For simplicity, I

consider one-sided interactions, where both the principal’s and the agent’s payoff

1 The story is true, but the names and details have been changed to protect the innocent.

2

are dependent on the hidden actions the agent takes. One can think of a large

number of symmetric interacting actors where random tasks arrive to randomly

assigned principals who must seek out an agent for its successful completion.

Agents come with different types. The principal would prefer to partner with

an agent suitable to the task but is uncertain of the agent’s type. Suitability is

defined as the agent that maximizes the principal’s expected utility. The

principal’s beliefs regarding the agent’s type are indicative of the strength of the

relationship. After the agent has chosen her action and the outcome of the task is

observed, the agent can choose to apologize, signaling her type for the purposes

of securing future interactions.

In the language of psychology, the apology shifts the principal’s attribution

of the cause of the task’s outcome, blaming the failure on random chance, i.e. the

situation, rather than the agent’s type, i.e. her disposition.

In the example above, Paul2 is randomly chosen as the principal and

assigned the task to find somebody to meet to play tennis. Paul chooses Amy to

be the agent based on his beliefs regarding her punctuality, i.e. her type. During

the first two apologies, Paul is willing to attribute the lateness to random

justifiable events, for example traffic. After the third time, Paul concludes that he

was wrong with his earlier attributions and potentially ends the relationship.

In this paper, I establish a general framework for thinking about apologies

applicable to a broad class of games, and then propose and examine several game

theoretic mechanisms that describe the apology interaction. I begin with the

simplest model, and suppose that an apology is a costly signal where “good”

types find it easier to apologize, in the spirit of Spence (1973; etc.). I then build

on that framework and consider a typology of apology mechanisms that allows

me to endogenize the cost. By introducing a second dimension of type to

preference alignment, call it control or status, I offer a cheap talk model of

2 I am well aware that I am confounding gender roles by making the principal a “he” and the agent a “she” but it was a true story, and I believe that true gender equality means it should not matter.

3

apologies. I also briefly outline two alternatives based on social contracts, and

finally empathy.

In the sparse psychology and sociology literature, as well as through

introspection, various properties of apologies can be extracted and various

questions that can be asked in a rational framework can be raised. Why do people

apologize? When do people apologize? Why are they accepted? When are they

accepted? What is the cost of an apology? What is the benefit? Why does the

impact of apologies deteriorate with time? Importantly, if talk is cheap, then why

is it that people do not always apologize?

The fundamental goal of this project is to provide a framework for a rational

explanation that explains the workings of a social institution that is presumed to

be based on emotion. With an understanding of how the mechanism could work

given rational actors, then we can begin to understand how the mechanism arose

evolutionarily, and how and why we pass on notions of guilt and remorse to our

children. The ancillary goal is that in the process, I formally define common

notions such as mistake, sympathy, empathy, situation, disposition, and intention

in ways that make them tractable by game theory.

The purpose of the model is that it can be used to help understand important

policy questions. For example, the recent emergence of “I’m sorry” laws in

California, Massachusetts, Texas, Florida and other states that make apologies

inadmissible in courts. I also examine prominent political apologies. The popular

press does not understand why politicians never apologize. Additionally, I

consider the implications of apologies on organizational design. By making

formal terminology and systems that have previously only been informally

discussed, I seek to bring clarity to these issues.

The paper proceeds as follows: Section two presents a few important

concepts for thinking about apologies, and how those concepts will be used in

this paper. Section three contains a review of the broader social science literature

on apologies, followed by a review of the economic tools used in this paper, and

ends with a review of the psychological theory of attribution that is foundational

4

in informing the model. Section four presents the basic model of apologies with

exogenous costs. Section five provides several alterative specifications that

endogenizes the cost of apology. The first generalizes this model to a contracting

framework. The other two allow multi-dimensional type, the added dimension

representing first empathy and then competence. The paper concludes with an

analysis of several cases and a check of the empirical evidence.

2 Apology Concepts Everyone has some notion of what it means to apologize. In order to

crystallize ideas before proceeding, I lay out the framework that I will use for the

remainder of the paper. An apology occurs between two actors, a principal and

an agent. One can think of the principal and the agent as being selected at random

from a larger community where the principal needs a task accomplished and

solicits the agent. For simplicity, presume there are two types of agents (though

the results largely generalize), one of which has preferences better aligned with

the principal’s. Formally, let the agent’s type have increasing differences with

respect to the principal’s expected payoff in the agent’s utility function. In a

political game, this would be closeness of ideal point. In a standard principal-

agent framework, this would be the productivity of the agent. In a simple divide

the dollar game, this would be a Fehr-Schmidt (1999) or Becker (1976) style

altruism parameter. Social psychologists would call this type, the agent’s

disposition, and I will speak of good dispositions and bad dispositions. The

American Heritage Dictionary (2000) defines sympathy as “A relationship or an

affinity between people or things in which whatever affects one correspondingly

affects the other.” Thus, the type θ is also a measure of sympathy.

The broad sketch of the game proceeds as follows: nature draws the agent’s

type, θ , the agent chooses an action x , there is randomness imposed by the

environment in the form of another draw by nature, ω , and the outcome,

),( ωxy , is mutually observed by both principal and agent. An apology can be

put forward or not, and the agent receives continuation payoff, )(−v .

5

(Insert Figure 1 about here)

The model is essentially a signaling game appended to a moral hazard

problem. The action of the apology mechanism occurs primarily with the

signaling, and thus for much of the paper, I will consider a reduced form of the

game that takes the agent’s action as exogenously fixed. However, the action is

important because the opportunity must be provided for the agent to make a

mistake. The American Heritage Dictionary (2000) defines an apology as “An

acknowledgment expressing regret or asking pardon for a fault or offense.”

Regret or fault requires a mistake. A mistake for homo economicus is the

difference between what is ex post optimal and what is ex ante optimal. The

environment variable, ω , can represent either new information about the world,

or new thinking and better reflection by the agent.3 It is important for mistakes to

be modeled using a random move by nature, because alternatives such as off

equilibrium play or trembles presumes that mistakes occur with near zero

probability.

Thus, using this framework, an apology by the agent is an effort to signal

that her original choice of x represented good intentions. Effectively she would

have chosen a different x had she known the realization of the state of the world

ω . Social psychologists call this state, the situation.

The principal can either attribute a particular outcome, y to the agent’s

disposition, a low θ , or to the agent’s situation, a bad draw of ω . The resolution

of this dilemma is the subject of attribution theory (Ross, 1977; etc.) in

psychology whose findings are elaborated upon in the next section. An apology

is an attempt by the agent to shift the principal’s attribution from disposition to

situation.

The precise specification for an apology differs in each of the four

treatments offered here. However, the commonality is that an apology entails a 3 Another interpretation suggested by Bernheim and Rangel (2004) is that ω is a mood, a temporary shock to preferences that are not indicative of typical preferences. The setup

6

message, , where a one indicates an apology. One might argue that a

richer message space may offer different results, but especially for my cheap talk

models, as Crawford-Sobel (1982) shows, in a sender-receiver game with

imperfectly aligned preferences, only a finite number of different messages are

possible, and there are many equilibria. In this paper, I consider the equilibrium

where there are two messages. I also do not distinguish between a non-apology,

and inaction. I interpret inaction to be a message of

1,0∈a

0=a .

Another key component of an apology is its value in the restoration of

relationships (Tavuchis, 1991; Ohbuchi et al., 1989; McCullough et al., 1998;

etc.). The larger ecology of apology is beyond the scope of this paper, but if we

assume that actors attempt to maintain relationships with those of higher (more

aligned) type, then the principal’s beliefs regarding the agent’s type can be seen

as a measure of the strength of the relationship.

Finally, as this paper considers situations where payments between actors

are disallowed, is a payoff based on the probability the principal decides to

continue the relationship, i.e. forgive. Alternatively, it is based on the probability

that the principal stays with the same agent for this task, rather than switch to a

different one. At times, it will be useful to think of

)(−v

)(−v as the continuation

value of a stationary game where the above framework is a stage game. This

notion of forgiveness is very reduced form. A more in-depth study of forgiveness

in left for future research.

3 Literature Review

3.1 Applications To emphasize the import of apologies in many economic and political

interactions, I highlight six applications in particular.

would be slightly different than that which is presented here, but the analysis would largely be the same.

7

3.1.1 Interpersonal Relationships: Apologies are a common occurrence in everyday life, particularly in the

maintenance of friendships. Empathy is a particularly important component of

these apologies. Several questions will be addressed regarding cultural

differences in apologies—Asians apologize more than Americans (Takaku et al.,

2001; etc.)—or gender differences—women apologize more (Gallup, 1989 in

Tavuchis, 1991).

What psychology literature exists is focused on experimentally validating

stylized facts about the apology process. An apology by the agent reduces the

anger the principal feels toward the agent as well as the principal’s desire to

punish (Ohbuchi et al., 1989). In tasks where the agent is less responsible or

where the offense is less severe, the apology is rejected less often (Bennett and

Earwalker, 2001). Apologies are almost always accepted (Mullet et al., 1998;

Bennett and Dewberry, 1994). Forgiveness occurs more often in closer

relationships (McCullough et al, 1998).

The results of all the psychological experiments I found were consistent

with the findings in the models presented here.

3.1.2 Organizations: The prevalence of apologies in various organizational settings is indicative

of differences in task assignment, in risk taking, in turnover, etc. A coherent

model of apologies offers insight into cultural differences in organizational

design.

Lee and Tiedens (2001a) find that within an organization, when individuals

of high status—those with control—make excuses for their behavior, they suffer

a decrease in status.

3.1.3 Corporate Governance: CEOs are expected to be responsible to shareholders. When performance is

low or scandal arises, should an apology be expected? Does an apology carry any

weight? Lee and Tiedens (2004) find that kinds of attributions for past

8

performance found in company annual reports—effectively kinds of apology—

can predict a firm’s stock prices one year out.

The failure of business ethics due to the economist’s profit maximization

assumption has received recent attention (Ghosal, 2005). Apologies can be used

to reflect a firm’s ethical domain.

3.1.4 Politics: There is a stylized fact that politicians never apologize. Consider, Bush on

Iraq, Clinton on Lewinsky and Berlusconi on Germany. Lee and Tiedens (2001)

conducts an experiment where she constructs two videos, one where Clinton

appears to apologize regarding the Lewinsky affair, and one where he appears

angry. Subjects who saw apologetic Clinton liked him more, while subjects who

saw the angry Clinton liked him less and complained about how Clinton never

apologized. However, on questions of leadership, questions of ability, and

importantly, questions of whether you would re-elect, the angry Clinton did

better. Their result is robust to choice of politician and the crime.

3.1.5 International Relations: An apology by a government is important either between the government

and its people (e.g. South African apartheid, Japanese interment, or the United

States civil war), or between governments in international relations (the

difference between Germany and Japan’s response to World War II).

3.1.6 Law: In recent decades in the US, apologies have become increasingly important

in litigation damages. California, Florida and other states have recently passed

laws to prevent apologies from being considered as evidence in order to

encourage their use. Apologies are especially relevant in medical malpractice, as

a vicious circle has arisen. Doctors are afraid to apologize because of the large

risk of lawsuits. Patients are more likely to sue due to anger for not receiving an

apology. (Taft, 2000; Cohen, 2000; Latif, 2001; Cohen, 2002)

9

3.2 Mechanisms The psychology literature provides many properties of the apology

mechanism, but is largely deficient at systematically describing the process. One

common reason given for why people apologize is “negative affect alleviation.”

People feel guilty, and an apology removes the guilt (??,??). This view dates to a

Freudian model of human behavior where humans have stocks of emotion—in

this case guilt—which when accumulated, causes distress until emptied.

Tavuchis (1991) has an extensive sociological treatment of apologies, in

which he sees apologies as a complex social system designed to maintain

relationships and to establish membership in community. Tavuchis describes an

apology as a kind of social exchange, a device that somehow restores social order

paradoxically without altering the thing which is being apologized for. Nothing

material has been exchanged, yet the relationship has changed. An apology is

painful, and the pain is created by the social system of shame that accompanies it.

These psychological and sociological models of behavior, along with the

notion of behavioral scripts or heuristics pushed by Kahneman and Tversky

(1974; etc.) and others while not consistent with economic actors, may be

accurate. However, the model I propose is more teleological. In the mode of

Frank (1989), culture and evolution has provided devices such as guilt, remorse

and shame, in order to facilitate the apology mechanism for the purpose of

maintaining the social links that society depends upon. Thus, I retain the

assumption of rational actors for modeling purposes.

Attribution theory from social psychology is more useful for illuminating

how apologies work, though it is still incomplete. The main question addressed

by attribution theory concerns a situation when an outcome is observed—Amy is

late for a tennis match—that has two possible causes: dispositional—Amy is lazy

and inconsiderate—or situational—Amy was held up by unexpected traffic. Van

den Steen (2004) provides a rational explanation of the self-perception bias of

attribution theory which has observed that individuals tend to attribute their own

successes to their disposition while attributing their failures to the situation

10

(Bradley, 1978; Zucherman, 1979). This paper will address the fundamental

attribution error where individuals tend to attribute too much blame to the

disposition of the actor and not enough to the situation (Heider, 1958; Ross,

1977; Jones and Nisbett 1972). Further research refines this notion. The ultimate

attribution error (Pettigrew, 1979; Bodenhausen, 1988) argues that attributions

are made that assume the worst about an agent who is in the principal’s outgroup.

Weiner et al. (1987) applies attribution theory to the process of apologies,

and in experiments, finds that apologies that attribute bad outcomes to external

uncontrollable factors, ω , are more likely to increase liking than apologies that

attribute bad outcomes to internal controllable factors, x . This simple insight

demonstrates the basis of the models in this paper. Effectively, I argue that an

apology by an agent shifts the principal’s attribution of the cause of the bad

outcome to external factors.

3.3 Economics The closest economic literature gets to apologies, are the repeated game

strategies such as Tit-for-Tat studied by Axelrod (1984), etc., or the repeated

game punishment scenarios of Green and Porter (1984), etc. In this paper, I focus

more on the apology mechanism itself, a self-contained event that does not

depend on punishment or penitence. This paper also focuses primarily on

rational mechanisms, largely avoiding behavioral assumptions.

The four models presented here elucidate four different mechanisms by

which apologies can operate. They are intended to be a typology of possible

apologies, and useful in illuminating how apologies function.

The base case is the simplest where an apology is a costly signal of type.

The cost can be either a tangible cost such as legal sanction, or a more behavioral

notion such as shame.

In the remaining models, an apology is cheap.

11

The second model generalizes the base case by considering the apology

mechanism as a social contract, and considering the properties of such a contract

that will ensure truthful revelation.

The third and fourth models allow apologies to be cheap by adding an

additional dimension of type. In the third model, actors are characterized as

having empathy or not. Empathy—the understanding of another’s situation or

feeling (American-Heritage, 2000)—is modeled as having knowledge by the

actor of the principal’s payoff in the actor’s information set.

In the fourth model, actors are characterized both by a preference alignment

dimension, θ , but also by a degree of control or competence dimension, η . An

apology shifts attribution from one characteristic to the other. Incentive

compatibility is maintained by the principal’s choice of future tasks. The fourth

model can be seen as an endogenization of the cost function used in the base

case.

4 Base Model

4.1 Setup The timing of the base model proceeds as in Figure 1. The utility of the

Agent is given by a linear combination of the agent’s utility from the inputs and

outputs, the cost of apologizing, and the agent’s discounted payoff:

(1) ))),(),(((1)()),,(,(),,( )( ωωδωθωθω ω xyabvcxyxuxU aA +−=

Nature sets the agent’s disposition, , who then chooses an

action, , to maximize her expected utility over possible realizations of the

situation,

, GB θθθ ∈

Xx∈

,Ω∈ω where )(~ −Fω . After observing the outcome, ),( ωxy , she

chooses to apologize or not, 1,0)( ∈ωa , and incurs the cost, )(ωc , only if

. 1=a

12

δ is the discount factor and reflects either time preferences or the likelihood

of repeated interaction, thus δ goes down as the number of other players

increases.

The principal observes only the outcome and whether the apology was

tendered or not, and from that updates his beliefs, , where is his prior: ),( yab p

(2) ),,|Pr(),( pyayab Gθθ ==

One can think of the principal maximizing his utility in each stage game

with the function given by:

(3) ∑=t

tt

P yyU δ)(

The agent’s type θ is a measure of preference alignment, in the following

sense. If we let ),( ωω xyE be invertible in x , then we can rewrite ),,( θyxEu

as ),(~ θEyu . By preference alignment, we mean ),(~ θEyu has increasing

differences in θ and . That is to say, higher agent types either value the

principal’s utility more, or it is easier for higher agent types to provide principal’s

with higher utility.

yΕ

This specification for the utility function and production technology is

somewhat awkward, but many common moral hazard situations are captured. For

example, the standard moral hazard with high and low productivity where x

represents effort:

(4)

⎩⎨⎧

<+>+

=

−=

KxKx

xy

xyxu

ωω

ω

θθ

,0,1

),(

),,(2

A second example is a political game, where there is a uni-dimensional

policy space, x represents the agent’s choice of policy, the principal has an ideal

point of zero, while the agents have ideal points away from zero, and θ/1

13

represents the agent’s ideal point. This functional form can also model the Paul

and Amy interaction, where x is the choice of departure time, and ω is the

amount of traffic:

(5)

⎩⎨⎧

>+<+

=

−+−=

KxKx

xy

xyxu

ωω

ω

θωθ

,0,1

),(

)1(),,( 2

A third example might have θ as an altruism parameter, and the task is

some noisy division of a pie, where the agent’s choice x is how much of the pie

the agent keeps for herself.

(6)

⎩⎨⎧

>+<+

=

+=

KxKx

xy

xyyxu

ωω

ω

θθ

,0,1

),(

),,(

Given that ),(~ θEyu has increasing differences, then, ),,( θyxU A also has

increasing differences, and so the agent always chooses that yields a

higher for the principal, and the agent always chooses that yields

a worse outcome for the principal. Note that increasing differences depends on

the lack of dependence of

Gθ *Gxx =

Ey Bθ *Bxx =

)(−v on type. This independence is assumed to

simplify the analysis and clarify the signaling mechanism. However, when

is taken as a continuation value later on, dependence on

)(−v

θ will be necessary.

The production technology, 1,0),( ∈ωxy is uniquely determined by the

agent’s action and nature’s draw of the situation. To simplify analysis, define:

(7) 1),(:

1),(:*

*

==Ω

==Ω

ωω

ωω

BB

GG

xy

xy

Then, assume that the set of states where the good type fails is a

subset of the set of states where the bad type fails, . Essentially, some

GΩΩ \BΩΩ \

14

states are just universally harder to succeed in than in other states. This

assumption is actually stronger than necessary, but it is intuitive.

Note, in this analysis presented, variables such as type and output are all

dichotomous, though these can be generalized to continuous variables without

any substantive change in the results.

The principal’s only action is to decide whether to continue or end the

relationship. As in the career concerns models of Dewatripont et al. (1999), there

exists a market of outside options that forces the princpial’s “payoff” to be

commensurate with his beliefs regarding the agent’s type. The principal’s action

is effectively constrained by a renegotiation proofness condition and outside

options.

In terms of the model at hand, the principal decides whether to continue

based on the chance to interact instead with an outside option: a competing

agent’s who’s prior is drawn from some distribution. The principal continues the

relationship if his beliefs about the agent’s type is higher than his prior regarding

the outside option’s type. This strategy establishes an exogenous probability of

whether the relationship continues as a function of the principal’s beliefs

regarding the agent’s type. This probability multiplied by the value of the

relationship to the agent justifies the exogenously defined ))(( −bv . The only

restriction on is that it be monotonically increasing in )(−v )(−b .

4.2 Cost Function This model restricts the dependence of the cost function to only the

situation, ω . Dependence on type or intention could easily be added, but only

complicates the issue without adding intuition. In this model, the cost of

signaling is tied more directly to the agent’s action rather than the agent’s type as

in traditional signaling models.

Additionally, the cost of apologizing is given exogenously instead of being

chosen by the agent. One might think it more natural for the cost to be chosen by

15

the agent, instead of being prescribed. For example, the agent could choose the

size of the box of chocolates, or a drug company with a defective product might

choose how long to hide the information before apologizing. However, since I

am interested in situations where pooling occurs, I would focus on equilibrium

where both types choose the same cost. In which case, one could think of the

exogenously given cost function, )(−c as the internal unobserved cost required

to achieve the equilibrium externally observed cost.

The cost function thus defined can have multiple interpretations:

4.2.1 Tangible Cost A tangible cost is the simplest burn money scenario such as gifts of roses or

some other symbolic gift or gesture. Amy stands outside in the rain until Paul

forgives her.

Alternatively, there can be legal sanction. An apology after a car accident

increases the probability of losing a lawsuit.

4.2.2 Ambiguity Resolution It is possible that the outcome is imperfectly observed, or observed but not

contractible, thus an apology is an admission of fault and resolves the ambiguity.

This still depends on their being some exogenous cost that is a function of the

certainty that a bad outcome was attained. An apology by a politician regarding a

policy failure confirms that the outcome really is a failure. An apology by a

defendant confirming his guilt establishes proof beyond a reasonable doubt.

4.2.3 Lying The word apology derives from the Greek for story. An apology is an

example of account giving or excuse giving. The cost of lying is the probability

the lie will be found out. Amy claims she was late due to traffic, but there is

some chance Paul will hear a traffic report and catch her lie. Or alternatively,

many argue that humans are evolved to be poor liars and dishonesty can be

detected by facial cues (Ekman, 1969; Frank, 1989). In either case, the possibility

16

exists that a lie will be found out, and the cost represents the punishment

associated with lying, determined socially outside of this model.

4.2.4 Status A common reason given that it is difficult to apologize is that an apology

entails a loss of status. This will be modeled more explicitly, effectively

endogenizing the cost, in Section 1.

4.2.5 Psychic Costs The costs can be entirely behavioral, whether through norms of shame that

surround the very act of giving an apology, mitigated by alleviation of guilt.

Tavuchis (1991) argues that society makes it painful to apologize through norms

of social disapprobation, because the pain is what gives apologies meaning. The

model here gives testament to this view of apologies. Again, although there is

considerable psychological and sociological evidence that such mechanisms are

at work, this paper focuses on rational explanations.

4.3 Analysis To simplify notation, recall is the principal’s prior and is the

principal’s posterior belief that the agent is a good type after observing the

outcome and the apology (or lack thereof). Define:

p )(−b

(8)

)0,0|Pr()0,0()1,0|Pr()0,1(

)1|Pr()1,0(

0

1

=======

=======

======

ayyabbayyabb

yyabb

G

G

Gg

θθ

θθ

θθ

In the case of success, 1=y ,4 we do not define a variable for beliefs in case

of apology, because we will show that agents never apologize in case of success.

4 This analysis could be extended to allow for a continuous range of y, rather than dichotomous. The result would have some y* above which both agents never apologizes (i.e. success), and below which they sometimes do (i.e. failure). Further, the principal has more information on which to condition his beliefs. Qualitatively, however, things look the same.

17

By definition of conditional probability,

(9) ]0Pr[]0|Pr[]1Pr[]1|Pr[ ==+=== yyyyp GG θθ

Solving the model by backward induction, the agent only apologizes if

(10) )()()( 01 ωcbvbv >−

The left hand side is independent of ω , so there is some cut point, where

the equation is satisfied. Define

*cAΩ to be the set of states of ω where

. *)( cc ≤ω

By Bayes’ Rule:

(11)

)1))(\()\(())\()\(())\()\((

)1)(\()\()\(

0

1

pFpFpFb

pFpFpFb

ABAG

AG

BAGA

GA

−ΩΩ∩ΩΩ+ΩΩ∩ΩΩΩΩ∩ΩΩ

=

−ΩΩ+ΩΩΩΩ

=

It is possible for corner solutions to arise where there is pooling and is

empty. The rest of the analysis assumes an interior solution.

AΩ

Note that non-empty and since AΩ )(−c is assumed positive we get

(12) 01 bb >

Which implies that good types always apologize more than bad types.

(13) ]|1Pr[]|1Pr[ BG aa θθθθ ==≥==

By the assumption that , the set of states of the world

where the good type apologies, , is weakly smaller than the set of

states where the bad type apologizes, . Even if both types always

apologize, then at best . If there were any states where an apology would

be too expensive for one type but not the other, it would only be in cases where

the bad type failed when the good type would have succeeded. Thus .

BG ΩΩ⊂ΩΩ \\AG Ω∩ΩΩ \

AB Ω∩ΩΩ \

pb =1

pb ≤1

18

Combining equations 9 and 12 allows us to write:

(14) 01 bbpbg >≥>

Successes strengthen relationships. In case of failure, apologies remedy the

relationship and restore the relationship but only imperfectly so. If we treat

as a continuation value and have the players myopically repeat the game, an

apology after one failure may restore the relationship sufficiently to continue the

game, but a succession of failures can leave low enough for the principal to

end it. Hence, Paul’s frustration after Amy’s third episode of tardiness.

)(−v

b

Taking the limit in equation 11 as goes to zero or to one, means the

priors begin to dominate the posteriors, which means the differences in beliefs

goes to zero. Thus

p

01 bb −

(15) 0)()( limlim10

=Ω=Ω→→

A

p

A

pFF

This implies that when the principal is fairly confident in the agent’s type,

the prevalence and impact of an apology goes to zero. Thus, the impact of an

apology is maximized when there is uncertainty about the agent’s type. When the

principal is fairly certain of the agent’s type, then the impact of an apology is

minimal, and thus the cost is not worthwhile. When the principal has decided that

the agent is no good, an apology will not change his mind.

Similarly, this result also implies that “Love means never having to say

you’re sorry” (Segal, Love Story, 1972). This second implication, however, is not

robust to all specifications. In fact, in the other models, love implies you always

apologize. However, this inconsistency reflects the inherent controversy of the

movie quote. Linguist Deborah Tannen (1996), for example, argues that Segal’s

quote is exactly wrong. The other models will better address her concerns.

The results are summarized in the following graphs:

(Insert Figure 2 about here)

19

4.4 Attribution Theory With this base model in hand, we can begin to consider the theory’s

implications in regard to attribution theory. The principal upon observing the

outcome can make two possible inferences, either the bad outcome was due to a

bad type, the actor’s disposition, or a bad draw of nature, the actor’s situation.

A simple by-product of the nature of the model is that in the absence of an

apology, the principal assumes the cause was situation. Essentially, our principal

commits the fundamental attribution error. The commission of this error is

somewhat a product of the model, but it is an essential product.

The intuition is that if some costly mechanism exists to change someone’s

beliefs, or attributions, then the default must be to think the worst of the other

person, otherwise they would have no incentive to correct the misattribution.

Thus when observing an agent fail at an action, we always assume the actor was

at fault, because had we assumed it was the environment, the agent would have

no incentive to correct it, and the environment is by definition incapable. This

interpretation of attribution is consistent with the extensive evidence though it

applies only to failures. You would expect the opposite biases in attribution when

it comes to successes. Most of the experimental evidence has focused on the

negative. Furthermore, studies involving the ultimate attribution error and hostile

attribution bias confirm this asymmetry (Pettigrew, 1979; Bodenhausen, 1988;

etc.).

Though this model does not address self-perception bias—people attribute

their own successes to their disposition, and their own failure to the situation—

the same intuition applies. Incentives need to be provided to others to correct the

misperceptions, and if no correction is forthcoming, then we are right to adjust

out attribution accordingly.

Psychologists have been good at identifying sources of bias in human

decision making but have largely ignored the question of why these biases exist.

The model presented in this paper demonstrates that the bias exhibited in the

fundamental attribution error is not a mistake, but a rational response given a

20

fuller understanding of the social interaction. The model also allows predictions

as to when the fundamental attribution error is more likely to be observed. In

addition to the asymmetry between positive and negative outcomes, the error is

most likely to occur when uncertainty about the other’s type is highest. The error

is also likely to be more pronounced when the cost of apology is high, such as

when individual status is more important that community relationships. Since

Asian cultures tend to exhibit far more apologies than Western cultures, one

would expect Westerners to commit the fundamental attribution error more often.

Psychological research bares these predictions out (many cites here, ????).

It should be admitted that in laboratory settings, subjects should be aware

that no apology is possible, and so a rational actor should not be subject to such

effects. However, one can presume that these beliefs arise from heuristics

developed for the real world, and thus are short circuited in laboratory settings.

5 Cheap Apologies The model presented in the previous section is effective at explaining many

of characteristics observed in apology interactions. However, its reliance on an

externally given cost function leaves the modeling unsatisfying. In this section, I

return to the question originally posed: if talk is cheap, why do apologies have

any meaning? From here on out, an apology will simply be a message, and its

meaning will be derived in equilibrium. I begin with two alternative mechanisms

based on social contracts and empathy. I then finish with a status model that

endogenizes the cost in the base model using multi-dimensional type.

A note on continuation values: For the remainder of the paper, it will be

convenient to think about )(−v as a continuation value, and thus it is necessary

to introduce the dependence on type, thus we have ),( θbv . The main problem

here is that this dependence may induce strange behavior in that it may

encourage good types to purposefully fail at the task in order to signal her type.

However, recall that is discounted by )(−v δ . In all future examples, assume δ

sufficiently small so that increasing differences still holds, so that the good type

21

will always produce better results for the principal. That is, presume either

sufficiently impatient actors, or, better yet, presume a large enough community

that ensures frequency of interaction to be sufficiently rare. Note, that this

assumption only impacts the moral hazard part of the model. The apology

signaling mechanism payoffs occur all in the same period, and thus are

unaffected.

5.1 Status A common reason that is given as to why apologies are difficult is because

an apology entails loss of status. One could argue that the reason women

apologize more than men is because evolutionary pressure has made status more

important for men, because men need status to compete for mates. Thus, since

status matters relatively less for women, they can apologize more. The same can

be said for Asian cultures relative to Western ones. If Asian cultures value group

preference alignment more than individual ability, then apologies will be more

prevalent in Asian cultures. Social psychologists have also found that culture

matters in attribution error (Markus and Kitiyama, 1991; Nisbett, 1993). For

example, Iyengar and Lepper (1999) find that Asians are less likely to commit

the fundamental attribution error providing further evidence of the connection

between attribution and apology. This section will formalize the notion of status

and by doing so, provide a more compelling reason why cheap talk apologies are

effective.

Tiedens (2001) experimentally demonstrates that even though politicians

gain approval and liking by apologizing, a apology causes the politician to lose

status as measured by respect or willingness to re-elect. Up until now, the point

of an apology was to shift the principal’s attribution of the cause of a bad

outcome from an internal controllable quality of the actor, to an external

uncontrollable quality of the environment. Lee and Tiedens (2001a) find that

even a successful shift of attribution may not be a good thing for the agent, if the

agent is expected to have control over the environment. They find no such

downside to apologies when the agent is not expected to have control.

22

5.1.1 Setup To model this quality of control, consider another dimension of type for

control called which represents either high control or low control.

For the rest of this section, I will assume a specific functional form for simplicity.

Let the alignment type be

, LH ηηη∈

(16) −∞=

=B

G

θ

θ 1

and let the control type be

(17) ∞=

=L

H

η

η 0

Restrict the action space so that 1,0∈x which represents either positive

effort, , or no effort, 1=x 0=x .

Let the utility function5 be given as

(18) ),,,(),,,( ηθδηθηθ ηθ bbvxyyxU A +−=

Finally, let the production technology be simply

(19) xxy =),( ω

Note that for the purposes of this example, I ignore randomness in situation.

I do this in order to limit attribution to two possibilities again, thus simplifying

analysis. Aligned agents want the same outcome as the principal, while

misaligned agents will do anything to avoid it. However, only high control agents

are capable of producing.

For this model, I will treat )(−v as a continuation value and give the

principal a more sophisticated strategy. There could be multiple stages, but I will

restrict to two periods for illustration purposes. In the second period, there is no

5 So θ and η cannot technically take on infinite values as they occasionally need to be multiplied by zero. Assume very large numbers instead.

23

)(−v

), ii

. The principal, now, instead of deciding whether to continue or discontinue

the relationship, chooses instead which task to offer.

As one further addition, instead of assuming that tasks are identical, I

instead assume that there is a sequence of possible tasks. For each task, , the

agent has a pair, (

i

ηθ . For simplicity, let the prior for all θ be and let the

prior for all

p

η be . The principal does not know the values of the agent’s types,

only the priors. The agent does know the correlation between any two tasks,

however:

q

(20) ],[, jiji Corr ηηφ

],[, jiji Corr θθρ

=

=

For example, after playing tennis with Amy, Paul does not know if she will

be late for lunch, but he does know that chronic lateness for tennis is highly

correlated with chronic lateness for lunch.

5.1.2 Analysis Given these extreme parameters, first period output is given by

η yθ G H 1 G L 0 B H 0 B L 0

Output is only produced if both preferences are aligned and the agent is in

control. Given these payoffs, a simple equilibrium strategy for the principal is to

assign tasks based on the following rule:

• If choose a task with 1=a 0,1 == φρ

• If choose a task with 0=a 1,0 == φρ

In words, if the agent apologizes, offer her a task that is perfectly correlated

along the alignment dimension, if the agent does not apologize offer a task that is

perfectly correlated along the control dimension. In Tiedens’ (2001) political

24

example, if the politician apologizes, offer him a task in the next period based on

character, such as dating your daughter. If the politician does not apologize, offer

him a task in the next period based on control or ability or competence, such as

running the country.

The agent only receives positive utility if both her preferences are aligned,

and her control is high. The second period payoffs for an agent are:

(21) )|Pr()|Pr( 1212 ηηηθθθ HGAU ===

Thus, given the above strategy of the principal, the second round payoffs for

an agent who failed are

θ η yE a 1| = yE a 0| =

G L q 0 B H 0 p B L 0 0

Thus assuming indifference is properly resolved, good types will always

apologize, while bad types will not. More generally, for any arbitrary correlations

),( ,, jiji φρ for the next task, the payoffs to the agent will be

θ η Ey G H )]1()][1([ qqpp −+−+ φρ

)]1()][1([ φρ −−+ qppG L B H )]1(1([ qp )][q −+− φρ B L )]1()][1([ φρ −− qp

Thus, the principal can maintain this cheap talk equilibrium so long as he

offers two tasks that satisfies the proper incentive constraints. Assume the

principal focuses on choosing tasks that separate the ( types from the

types. Whether the ( types apologize will depend on the tasks

available.

), LG

),( HB ), LB

One can think of a larger ecology of actors, where each period, a randomly

chosen principal has a task that requires an agent. If there are a sufficient number

25

of diverse agents the principal can choose from, then the principal can commit to

assigning that task only to an agent where the correlations satisfy the IC

constraints from their previous interaction.

Other things to consider is that if there were added an additional exogenous

cost of apology, such as the legal sanctions from before, then this would shift the

set of tasks that satisfy the IC constraints. Laws that change these costs could

again impact this interaction.

Additionally, it should be noted that apologies will generally increase liking,

as θ ’s are updated upward, while non-apologies will do the opposite. Also, any

particular action will in fact shift beliefs about all other tasks via the correlation

matrix, thus complicating analysis if extended to more than two periods, though

not substantively so.

Thus, returning to the aforementioned gender and cultural differences, men

apologize less because they value tasks that depend on control more than women.

In Asian cultures, tasks are primarily based on preference alignment, and

individual initiative is deemphasized, thus making apologies more common.

5.2 Alternative I: Social Contracts There are two alternatives to adding a dimension of control to type. The first

depends on allowing the principal to commit to changing the payoffs in future

periods.

Generalizing the model from section 4, it is possible to effectively subsume

the cost of apologies into the continuation value, and think about specifying

as some sort of social contract that maintains the apology mechanism.

Then, what is necessary is to have a payoff function,

)(−v

)(−v , such that the

following incentive compatibility constraints are satisfied:

(22) ),1()(

),0()(

1

1B

aa

Gaa

bvbv

bvbv

θ

θ

=≥

=≥

=

=

,0

,1

1

1B

G

θ

θ

=

=

=

=

26

One such way to obtain such a payoff function in the first stage is to have a

two-period game with appropriate payoffs in the second stage. I call this a “fool

me once, shame on you, fool me twice, shame on me” contract. The intuition is

that the principal would like to know the private information of the agent, but the

agent has incentive to misrepresent her type, so an apology is a claim to be a

good type. However, if the agent claims she is a good type, the principal will

demand much more out of the agent, and tolerate failure far less, whereas if the

agent does not apologize, the principal will be more forgiving of failure. The

following is an illustrative example.

(Insert Figure 3 about here)

Assume for simplicity that preference alignment is strong enough that

second stage probability of success is fixed at for the good type and for

the bad type. Then to satisfy the IC conditions in the first stage, we need:

Gs Bs

))(1()(

))(1()(

0,00,01,01,1

0,00,01,01,1

========

========

−−≤−

−−≥−

yayaB

yayaB

yayaG

yayaG

vvsvvs

vvsvvs(23)

Effectively, since , the marginal benefit of success in the second

stage in the case of an apology in the first, must be higher than the marginal

benefit in case of no apology in the first.

BG ss >

There are issues of renegotiation proof-ness that will not be dealt with here.

5.3 Alternative II: Empathy In this section, I consider again the possibility of another dimension of type,

but instead of control, I consider empathy, which will be a reflection of the

information structure of the game.

Though the primary purpose of an apology, and the primary dictionary

definition, is in relation to a fault or offense, the notion of apologies is often

conflated with a general sense of empathy, or awareness of the other’s emotional

state: “I am sorry to hear that your grandmother died.” Specifically, this section

27

tries to understand partial apologies, those apologies that do not come with an

admission of guilt.

Alternatively, empathy can be interpreted as awareness of the agent of what

the principal considers appropriate rules of conduct. The apology act could be an

implicit part of some bargain over appropriate norms of behavior.

To capture this interaction, in addition to a preference alignment type, θ , let

there be an empathy type, 1,0∈τ , where empathic and non-empathic types

differ only in their information sets; non-empathic types do not observe the

principal’s payoff, y .

Again, empathy could be made a continuous variable by specifying

information sets over states of the world, ω , rather than outcomes, y , with

agents that have greater empathy having a finer partition. However, I again favor

simplicity.

To make empathy relevant, let there be a positive correlation, ψ , between

the two types, either because the empathic types are more effective at producing

given their better understanding of the principal, or for some external common

reason such as better upbringing.

In such a game with cheap apologies, consider an equilibrium where

empathic types always apologize in case of failure, and never apologize in case

of success, and non-empathic types never apologize.

Given such an equilibrium, the principal’s beliefs of the agent’s empathy

will be (with prior on q=τ ):

(24)

qyayaya

a=

y

=================

|1|1

τ

]1Pr[]1,0|1Pr[1]0,1|1Pr[

m)equilibriu-(off 0]0,0Pr[m)equilibriu-(off 0]1,1Pr[

τττ

τ

An inappropriate apology automatically gives the non-empathic types away.

An appropriate apology proves empathy, and conveys information on preference

28

alignment via the correlation with theta. Then, the principal’s updated beliefs

regarding the agent’s preference alignment, θ , in such a game are:6

(25)

)1](|0Pr[)\(]|0Pr[)\(]|0Pr[)\()0,0(

)1](|1Pr[)\(]|1Pr[)\(]|1Pr[)\()0,1(

pFpFpFyab

pFpFpFyab

BBGG

GG

BBGG

GG

−==ΩΩ+==ΩΩ==ΩΩ

===

−==ΩΩ+==ΩΩ==ΩΩ

===

θθτθθτθθτ

θθτθθτθθτ

)1)(()()()1,0(

pFpFpFyab BG

G

−Ω+ΩΩ

===

Using the positive correlation between τ and θ we know that

(26) ]21]|0Pr[]|021]|1Pr[

BB

GG

θθτθθτ

θθτθθτ

==>==

==>==

)0,0()0,1(

|1Pr[Pr[

>

>

so we can get:

(27) ==>== yabyab

))0,1(()\())1,1(()())0,0(()\())1,0(()(

bvFbvFbvFbvF

ii

ii

ΩΩ+Ω>

ΩΩ+Ω

This equilibrium strategy is optimal for the empathic types, since in the

event of failure, the principal believes that the agent is a high type more if an

apology is given. The equilibrium strategy is optimal for the non-empathic types

so long as:

(28)

6 These expressions can be simplified using the fact that the conditional probability for two correlated Bernoulli variables with the same prior is given by

)1()1|Pr()1()1|Pr(

ψτθθ

ψτθθ

−===

−+===

ppp

H

H

29

Or re-arrange to get the probability of success times the marginal benefit of

apologizing in case of success must be greater than the probability of failure

times the marginal benefit of apologizing in case of failure:

(29) ))]0,0(())0,1(()[\())]1,1(())1,0(()[( bvbvFbvbvF ii −ΩΩ>−Ω

Essentially, if we assume that in most situations, the agent is successful and

thus an apology is unwarranted, then the non-empathic agent finds it optimal to

never apologize to avoid revealing her lack of empathy.

It is useful to note that once the apology is made, in a simplified model

without any further noise and empathy is stable across time, the principal learns

for sure that the agent is empathic. Thus over repeated interactions, the principal

quickly becomes aware that an agent is empathic. However, repeated failures

would still lead the principal to conclude the agent is a bad type, and thus the

principal will end the relationship anyway. This rapid devaluation of the

perfunctory apology corresponds to the real world observation that often such

apologies seem meaningless. Once empathy has been established, further

apologies have little impact on the principal’s beliefs regarding the agent’s type.

The relatively minor impact of apologies in this scenario accords with the

assertion that these apologies—apologies without admission of fault—are only

partial apologies. However, if ever an agent fails to offer even a partial apology

when it is expected, judgments can shift quickly in this off the equilibrium path

scenario.

Another interpretation of this model is in the situation where an apology is

tendered before the principal is even aware of the mistake. In addition to the

tangible costs of ambiguity resolution (see Section 4.2.2), an apology also

demonstrates awareness than a transgression occurred and an apology is

warranted.

Alternatively, one might think of a world where different standards of

behavior are possible. In one culture, being an hour late is unacceptable while for

another, being an hour late is a virtue. An apology can be thought of as an

30

acknowledgement by the agent that she violated a norm according to the

standards of the principal. An apology indicates a shared agreement of the norms

of behavior, or at the very least, an awareness by the agent of what the principal

considers are the norms of behavior.

Incidentally, this model applies equally well for other perfunctory

pleasantries such as “thank you” or “congratulations.”

6 Discussion In this section, I consider the implications of the models presented on two

applications, the use of apologies in legal settings, and the implications of

apologies in regard to corporate culture.

6.1 Apologies and the Law One of the few areas of scholarly research that examines intensively the

question of apologies is in the area of law. Apologies have an important impact

on the outcome of cases. Unsolicited apologies can have an impact on conviction

rates, as well as sentence and judgment sizes (Rehn and Beatty, 1996).

Furthermore, even court ordered apologies appear to mitigate punishment (Latif,

2003). Yet as a result, many legal scholars (Cohen, 2002; Taft, 2000) worry that

by using apologies the courts are interfering with a “natural” process of social

remediation. This concern has prompted lawmakers to consider legislation that

exempts apologies from use in the courts. In this section, I examine the

implications of the model applied in the legal system.

The model provides several implications on the impact of apologies as part

of legal settlements. Consider sentences that mandate apologies. If there is a

fixed amount of punishment associated with any given crime, then one would

expect mandated apologies to be accompanied by lower sentences and smaller

fines.

31

The model also predicts that apologies have higher impact when there is

more uncertainty regarding the agent’s type. If one were to estimate a probit

analysis of an individual’s guilt based on the observable characteristics of the

case, then apologies should have a larger effect on sentences and fines for cases

with greater uncertainty. Flanagan (????) finds that the cases that do go to trial

are the most uncertain.

In order to assess the impact of an apology on legal outcomes, a central

tension between culpability, x , and character, θ , must be resolved. A fair

presumption might be that convictions and findings are based on culpability.

However, the size of the sentence or the award is based on character (????????).

Consider cases where an apology is voluntarily tendered. If an apology is

considered a partial admission of guilt, then one would expect voluntary

apologies to be associated with higher conviction rates, but lower sentences,

presuming the court would give leniency for good intentions.

Rehm and Beatty (1996) suggest one way to separate the culpability

dimension from the moral character dimension by considering attorney discipline

cases where the court decision should be based only on character. Using case

studies, they argue that in such cases, apologies always help.

The consequences of apology are of special concern in the area of medical

malpractice. Doctors are typically told to avoid admissions of fault, and

apologies in particular, because of the risk of lawsuits (Pinkus, 2000; Novack et

al., 1989). Yet patient lawsuits in the event of error are rare, and only occur when

the patient has a poor relationship with the doctor (Gallagher et al., 2003; Huycke

and Huycke, 1994). A lack of apology often is the reason why a lawsuit is even

filed (Hickson et al., 1992; May and Stengal, 1990). Thus the lack of apologies

often results in a vicious cycle that recent “I’m sorry” legislation hopes to break

(Cohen, 2003). States ranging from Massachusetts, Texas and California have

passed or are considering legislation that exempts expressions of remorse from

being used as evidence in civil cases.

32

A quick implication of this legislation is that in states where “I’m sorry

laws” have been implemented, a voluntary apology should have no impact on

evidence, but potentially gives information about intentions. If intentions did

matter in determining conviction, then voluntary apologies should then be

associated with lower conviction rates, relative to voluntary apologies in other

states.

The “I’m sorry” laws can be modeled using the base model as an exogenous

shift in the cost function. If we presume that the natural process of remediation is

based on psychic costs imposed by social norms, then the total cost of apology

will be legal costs plus psychic costs. Many of the legal reforms proposed will

reduce the cost of apologies in an effort to increase their use. Though the exact

effect is dependent on the shape of the reduction, it is useful to consider the case

where the cost is just a constant function: κω =)(c .

Then, a decrease in the cost of apologies, κ , will increase the likelihood of

apology, but it will also decrease the benefit, 0b1b − , that an apology induces.

Apologies will have less impact, potentially counteracting the reform. The

attenuated impact of an apology is reflected in moral arguments made by Taft

(2000) that apologies have been subverted by the legal system. Taft argues that if

laws specially exempting apologies from the legal system, apologies would lose

part of their moral weight that comes from the associated responsibility that an

apology entails.

Furthermore, a decrease in the cost of apology will reduce the costs

associated with failure, thereby decreasing the incentives in the action stage, and

increasing the equilibrium probability of failure. This increase in moral hazard is

echoed by Cohen (2002) who worries that the predicted decrease in law suits

files will have a detrimental impact. Already, very few cases of medical

malpractice come to trial (Huycke and Huycke, 1994). One could argue that since

these lawsuits are essential for restorative justice and efficient monitoring,

welfare would be enhanced if there were more lawsuits, not fewer.

33

Another quick testable implications, in states where such laws have been

passed, apologies should be more common, but at the same time less effective.

Thus the fraction of patients that pursue lawsuits given an apology should

increase.

One point of note is that except for Connecticut and Hawaii, the “I’m sorry”

legislation in most states exempt only partial apologies, that is apologies that

contain no admission of guilty (Cohen, 2002). Thus, one might say that the

empathy model (Section 5.3) might be more applicable.

6.2 Apologies in corporate culture Another natural venue where apologies are likely to be observed is within an

organization. Corporate culture is question oft posed in economics but has yet to

be fully answered (Kreps, 1986; Lazear, 1989; etc.). One way to tackle corporate

culture is by observing that in certain organizations, apologies are common,

while in other organizations, apologies are uncommon. A natural question to ask

is what are the correlates with the prevalence of apologies.

This section is going to make the argument that the root of corporate culture

is fundamentally economic. The basic argument is that the optimal production

technology for a given firm is given exogenously. The production technology

implies a given pay structure. The pay structure attracts a particular workforce

composition. The pay structure and the workforce composition both lead to firms

to adopt what the organizational behavior literature calls either a masculine or

feminine corporate culture.

The model provides two reasons why apologies would be common in a

given organization. The first is that the cost of apology is low: either the norms

specify only minor social disapprobation associated with apologies, or status is

not valued. The second reason for common apologies is that the benefits of

maintaining relationships are high. Both reasons can also be understood in the

context of the status model in an environment where activities that depend on

preference alignment are more prevalent that activities that depend on individual

competency.

34

6.2.1 A gender based typology Consider two firms, firm M and firm F. Firm M has a production technology

that stresses individual achievement. Either output is easily contractible or

observable, or there are few complementarities in output between workers.

Examples would be a sales department based on commission, or manufacturing

jobs that typically pay on piece rate. Compensation in firm M is associated with

individual achievement while relationships are devalued. Firm M is likely to

attract employees that undervalue relationships but value personal control (low

θ , but high η ). Firm F, on the other hand, has an optimal production technology

that emphasizes production in teams. Individual output is unobservable or

uncontractable and/or there are complementarities in production. Examples might

be marketing departments where creativity is emphasized, or workplaces that

emphasize subjective performance evaluations. Firm F is likely to attract

employees that have a high value of relationships relative to individual control

(high θ , relative to η ).

The model predicts that in firm F, apologies should be observed more often

than in firm M for two reasons. First, since firm F is likely to attract more high θ

individuals, the model predicts that high θ agents apologize more than low θ

agents. This is the selection effect. The second reason that firm F will have more

apologies is because a high θ is more highly compensated. Thus the incentives

to signal high θ are higher. In the base model, this comes from a higher marginal

return to a principal’s belief that the agent is of high type, i.e. high dbdv . In the

status model, this comes from higher returns or higher likelihood of liking (θ )

based tasks relative to status/control (η ) based tasks.

Since firm F will have workers with higher θ , more sympathy, by our

definition of θ , then we would expect a more nurturing environment.

Furthermore, the proximate cause of apology is associated with guilt, and thus we

would expect guilt to be more prevalent. Conversely, firm M would have a

culture that places a greater emphasis on pride and individual achievement.

35

Additionally, as in Lee and Tiedens (2001), the response to failure is more likely

to be anger rather than contrition.

Past organization researches have characterized this typology of corporate

culture as being either feminine—where apologies are common—or masculine—

where apologies are not (????, ????; working on the refs here).

6.2.2 Apologies and authority If we considers an extension to the model, we could make additional

predictions about organizations and project choice. Consider now the question of

organizational design, and consider the apology interaction to be a second stage

sub-game, where in the first stage, the agent is given the authority to choose a

task. Tasks differ in terms of difficulty in terms of the equilibrium probability of

success or failure. We are interested here in the interaction between the cost and

the project chosen. If the cost of failure is too high, even a good agent may

choose a project that has low risk, i.e. a low chance of failure. An organization

where risky projects are optimal may encourage a culture of easy apologies, at

the expense of losing the potential gains from sorting that a high cost of apology

provides.

Thus, the model predicts that organizations that have team-oriented

production functions or risky project choices are more likely to have apologetic

culture, while organizations that have individual oriented production functions or

safer project choices are more likely to have unapologetic cultures.

6.2.3 External perception of corporate culture The Kreps (1986) notion of corporate culture is that culture is an asset that

represents something comparable to reputation and trustworthiness. If we think

about corporations caring about some other dimension besides profitability, then

some of the empirical findings about the impact of apologies on shareholder

value can be reconciled. This other dimension may be business ethics (Ghosal,

2005), or reputation (Kreps, 1986), or a long-view/high discount factor. Though

36

these last two should be incorporated into views on profitability, there could be

market imperfections or short-sightedness that prevent it.

Lee et al. (2004) find that apologies made in corporate annual reports do

have an impact on stock price. Specifically, they find that companies that took

responsibility for their own poor past performance had a higher stock price one

year later. Although there are significant statistical problems in their analysis, the

paper raises the interesting possibility that public apologies provide information

about some dimension of the company’s future profitability that is not

immediately reflected in current shareholder value.

Aaker et al. (2004) consider the relationship between a firm and its

customers by conducting an experiment where they set up photo developing

companies with differing characteristics, and attempt to measure the reputational

effects of an apology after an infraction (the photos were temporarily misplaced).

The provided models provide insight into the differential effect apologies have

on company reputation as a function of differing priors.

7 Future Research There is considerable room for future research. Amongst which includes a

generalization of the theory of dynamic signaling used in this model.

Additionally, a more complete model of the applications of apologies to legal

settings or corporate culture is in the works. The theory of apologies itself can be

generalized to have a better notion of forgiveness and a better notion of the

community of actors.

Formal empirical tests beyond the confirmation of pre-existing

psychological studies is another avenue being pursued. The theory could be

tested empirically by looking at court cases, political apologies or corporate

scandals. Alternatively, data could be collected by surveying the corporate

culture of existing firms. Finally, a controlled laboratory experiment is being

considered.

37

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1 Figures

1.1 Figure 1

P: b forms beliefs,

N: θ Type (Disposition)

A: x HiddenAction

A: a=0 takes action

N: ω Noise (Situation)

All: y Observe outcome

1

A: a=1Sorry

Not Sorry

1.2 Figure 2

Age

nt’s

like

lihoo

d of

apo

logi

zing

bad agent

good agent

Principal’s ex-ante beliefs/liking

Prin

cipa

l’s e

x-po

st b

elie

fs/li

king

2Principal’s ex-ante beliefs/liking

ucceedsagent s

agent doesn’t apologize

agent apologizes

Figure 3

v1,y

y=0

y=1

y=0

y=1

a=0

a=1y=0

y=1

v1,n

v0,y

v0,n

3